No 05

Vertical Mergers, Foreclosure and Raising Rivals’ Costs – Experimental Evidence

Hans-Theo Normann

September 2010

IMPRINT DICE DISCUSSION PAPER Published by Heinrich-Heine-Universität Düsseldorf, Department of Economics, Düsseldorf Institute for Competition Economics (DICE), Universitätsstraße 1, 40225 Düsseldorf, Germany Editor: Prof. Dr. Hans-Theo Normann Düsseldorf Institute for Competition Economics (DICE) Phone: +49(0) 211-81-15009, e-mail: normann@dice.uni-duesseldorf.de DICE DISCUSSION PAPER All rights reserved. Düsseldorf, Germany, 2010 ISSN 2190-9938 (online) – ISBN 978-3-86304-004-8 The working papers published in the Series constitute work in progress circulated to stimulate discussion and critical comments. Views expressed represent exclusively the authors’ own opinions and do not necessarily reflect those of the editor.

Vertical Mergers, Foreclosure and Raising Rivals’ Costs— Experimental Evidence

Hans-Theo Normann∗†

September 2010

Abstract

The hypothesis that vertically integrated firms have an incentive to foreclose the inputmarket because foreclosure raises its downstream rivals’ costs is the subject of muchcontroversy in the theoretical industrial organization literature. A powerful argumentagainst this hypothesis is that, absent commitment, such foreclosure cannot occur inNash equilibrium. The laboratory data reported in this paper provide experimentalevidence in favor of the hypothesis. Markets with a vertically integrated firm are sig-nificantly less competitive than those where firms are separate. While the experimentalresults violate the standard equilibrium notion, they are consistent with the quantal-response generalization of Nash equilibrium.

JEL – classification numbers: C72, C90, D43

Keywords: Experimental economics, foreclosure, quantal response equilibrium, raisingrival’s costs, vertical integration.

∗Duesseldorf Institute for Competition Economics (DICE), University of Duesseldorf, Germany, Fax: +49211 8115499, email: normann@dice.uni-duesseldorf.de.†I am grateful to Dirk Engelmann, Wieland Muller, Martin Sefton, Georg Weizsaecker, and seminar

audiences at ESA Amsterdam, DIW Berlin, TU Berlin, University of Goettingen, Royal Holloway CollegeLondon, University of Mannheim, and University of Zurich for useful comments. Thanks also to VolkerBenndorf, Nikos Nikiforakis, Holger Rau, Silvia Platoni and Brian Wallace for their help on the research.Financial support through Leverhulme grant F/07537/S is gratefully acknowledged.

1 Introduction

The theoretical industrial organization literature has suggested that “raising rival’s costs”

may be a profitable strategy in oligopoly. Raising-rival’s-costs arguments are based on the

simple fact that it is easier to compete with less efficient firms. If a firm’s production costs are

raised, it will reduce output and increase price, and the other firms in the market will benefit

from this as they can increase their market shares and prices. It follows that firms may pursue

strategies from which they do not benefit directly (e.g. through production efficiencies) but

rather indirectly because a competitor’s costs are affected negatively. Cost-raising strategies

were first proposed by Salop and Scheffman [1983, 1987] and include boycott and other

exclusionary behavior, advertising, R&D, and lobbying for standards and regulation.

Ordover, Saloner and Salop’s [1990], henceforth OSS [1990], raising-rival’s-cost paper has

received particular attention because it sets out to establish a connection between vertical

integration and foreclosure.1 In OSS [1990], foreclosure means that a vertically integrated firm

withdraws from the input-good market, that is, it stops supplying the input to nonintegrated

downstream firms. OSS [1990] argue that firms have an incentive to integrate vertically

and engage to in such foreclosure because they gain from a raising-rival’s-costs effect. The

logic is that, when a vertically integrated firm forecloses, competition in the input-good

market becomes weaker. The reduction in competition implies higher input costs for the

nonintegrated downstream firms. Since the downstream unit of the integrated firm benefits

when downstream rivals’ costs are raised, the integrated firm is better off with the foreclosure

strategy than when it actively competes. In other words, it pays for the integrated firm

to forgo business in the input-good market and instead to gain because the downstream

rivals become less competitive. Only a vertically integrated firm can pursue such a strategy

profitably. It would not make sense for nonintegrated upstream firms to foreclose (they would

simply lose money) nor would this strategy be feasible for nonintegrated downstream firms.

1Salinger [1988], Hart and Tirole [1990] and OSS [1990] are the first generation of post-Chicago foreclosure

theories. See Rey and Tirole [2007] or Riordan [2008] for recent surveys.

1

Consumers

U2

D1 D2

U1

Consumers

U2

D1 D2

U1

A. Nonintegration B. Integration

Figure 1. Market structure

?

Figure 1: Market Structure

Consider OSS’ [1990] setup as shown in Figure 1. There are two upstream firms and two

downstream firms. In panel A, neither firm is vertically integrated and both upstream firms

compete for both downstream firms. For example, if the two upstream firms are Bertrand

competitors, the input market will be perfectly competitive. Now suppose U1 and D1 merge

as in panel B of Figure 1. Since U1 will supply D1 with the input internally, U2 can no

longer compete for D1. More importantly, if U1-D1 stops delivering D2 (or alternatively if

it charges a very high price for the input), U2 will increase its price above that before the

merger and U1-D1 will benefit from this price increase because D2’s increased input costs

ultimately improve U1-D1 profits—this is the raising-rival’s-cost effect.

Researchers soon argued that there is a problem with this argument. Hart and Tirole

[1990] and Reiffen [1992] pointed out that, even though foreclosure would be a profitable

strategy for the integrated firm, it still has an incentive to compete in the input market.

The outcome OSS [1990] derive is therefore not a Nash equilibrium. To understand this

argument, note that, given that the integrated firm withdraws from the input-good market

2

and U2 becomes a monopolist supplier of the input for D2, the integrated firm has an

incentive to deviate. Rather than stay out of the input market, it will compete in order to

gain the business with D2. U2 will anticipate this and then the Nash equilibrium is the same

both with and without vertical integration.

The problem with OSS [1990] is actually more subtle than the last paragraph (and the

discussion in much of the literature) suggests. OSS [1990] assume that a vertical merger

enables a firm to commit to not delivering to the downstream rival (D2 in Figure 1). When

such commitment is available, there is no formal problem with the OSS [1990] argument and,

indeed, the integrated firm will foreclose the market. In that case, the raising-rivals’-costs

effect will result. However, Hart and Tirole’s [1990] point is not whether commitment works

but whether it will be available at all. They conclude that “commitment is unlikely to be

believable” [Hart and Tirole, 1990].

The availability of commitment also concerns OSS [1992], which is a reply to Reiffen’s

[1992] comment. OSS [1992] show that their results hold when upstream firms bid for a

nonintegrated downstream firm in a descending-price auction. Yet, to some extent, this

merely circumvents the problem that the original analysis posed. In the descending-price

auction, the integrated firm will drop out early in the auction, the input market will be

monopolized by the non-integrated upstream firm and, hence, the outcome is as in OSS

[1990]. Note that a deviation from this equilibrium is prevented by the rules of the auction.

By dropping out, the integrated firm commits itself not to compete. Whether the integrated

firm can commit is still subject to debate.2

Despite this criticism, OSS’ [1990] is a seminal paper in the theoretical Industrial Orga-

2Similar criticism could also be made of related approaches that attempt to rectify OSS’ [1990] conclusion.

Choi and Yi [2000] and Church and Gandal [2000] assume that upstream firms can commit to a technology

which makes the input incompatible with the technology of nonintegrated downstream firms, in which case an

outcome similar to the one proposed by OSS [1990] results. As with OSS [1990, 1992], the central assumption

is that come form of commitment is available.

3

nization literature. It is the basis of the EU’s recent Non-Horizontal Merger Guidelines3. It

is featured in various textbooks and it remains a fruitful agenda for theoretical research. For

example, Linnemer [2003] simply assumes that a raising-rival’s-cost effect of vertical integra-

tion exists, and he uses this as a base for further theoretical analysis (see also Buehler and

Schmutzler [2005]).

The continued interest suggests that there may be more to the OSS’ [1990] hypothesis

than would come from a model that is plainly wrong. OSS [1992] themselves make such a

claim in their reply to Reiffen [1992], and, perhaps somewhat surprisingly for mainstream

theorists at the time, they use a behavioral argument when defending their position:

“The notion that vertically integrated firms behave differently from noninte-

grated ones in supplying inputs to downstream rivals would strike a business per-

son, if not an economist, as common sense” [OSS, 1992).

One interpretation of this quotation is that OSS [1992] suggest that their model may have

predictive power even though their scenario cannot be supported in a Nash equilibrium. (It

should be added that, as noted above, OSS [1992] propose the descending price auction where

the foreclosure effect does occur in Nash equilibrium.)

The quotation from OSS [1992] may also suggest that there are actually two interpre-

tations of the foreclosure notion. Foreclosure in a narrow sense can be said to occur when

integrated firms refrain completely from supplying the input market. In OSS [1990], the

integrated firms charge a price above the monopoly price U2 would choose—a strategy which

is equivalent to the exit of the integrated firm from the input-good market. A broader inter-

pretation of the term would be that integrated firms “behave differently” from nonintegrated

firms, that is presumably charge higher prices, but they need not completely foreclose the

3See the “Guidelines on the assessment of non-horizontal mergers under the Council Regulation on the

control of concentrations between undertakings”, Official Journal of the European Union, 18.10.2008, C265/6-

25.

4

input market. Broadly speaking, as long as vertical integration causes input prices to be

higher than those in markets where firms are separated, foreclosure occurs. Rey and Tirole

[2007] define foreclosure in the same broad sense.

This paper reports on an experimental analysis of the OSS [1990] argument. The experi-

ments were designed to investigate whether vertical integration per se affects the behavior of

integrated firms in the original OSS [1990] setup and does this without requiring any formal

commitment. The experimental design allows us to study the effects (in otherwise identi-

cal markets) of vertical integration compared to non-integration.4 Even if the static Nash

equilibrium does not predict an effect of vertical integration, experimental data may reveal

whether vertical integration results in foreclosure in the broad sense or the narrow sense.

Another contribution the paper makes relates to repeated interaction. The arguments

in OSS [1990, 1992], and in most of the theoretical literature, are based on the one-shot

game. However, interaction in the field is often repeated. Studying a repeated setting seems

particularly relevant here, since the commitment problem of the integrated firm may be

resolved with repeated interaction. After all, repeated interaction (Macauley [1963]) can

serve as an informal commitment device. Here, it may help the integrated firm to establish

a reputation for foreclosure. Experiments with repeated firm interaction investigate this

hypothesis. They are related to the recent theoretical literature that argues that vertical

integration facilitates collusion (Nocke and White [2007], Normann [2009], Riordan and Salop

4The effect of vertical integration has been analyzed in experiments before. Mason and Phillips [2000] study

a bilateral Cournot duopoly when there is a (large) competitive market that also demands the input from the

upstream firms. Durham [2000] and Badasyan et al. [2009] compare integrated and nonintegrated monopolies

and investigate whether vertical integration mitigates the double marginalization problem. Martin, Normann

and Snyder [2001] analyze whether an upstream monopoly loses its monopoly power when selling a good

to multiple retailers using two-part tariffs. None of these experiments have investigated the OSS [1990]

hypothesis and the design of the experiments would not be suitable for doing so.

5

[1995]).5

The design of the experiments in this paper follows the distinctions between vertical

integration and separation and between the static and the repeated game. The first two

treatments allow markets where both firms are vertically separated to be compared to markets

where one firm is vertically integrated under a random-matching scheme, such that incentives

are as in a one-shot game. Treatments three and four make the same comparison with a

fixed-matching scheme in order to allow for repeated-game effects. This yields a two-by-two

treatment design with vertical integration and the matching scheme as treatment variables.

The experimental setup is simplified as far as possible with the goal of providing a clean

test of the commitment issue, which is at the heart of the debate around the OSS [1990]

model. Only upstream behavior (the input market) is part of the experiment, because “how

input prices are set is a crucial determinant of the overall game” OSS [1990, p. 133]. A

Bertrand duopoly experiment was designed to address the foreclosure issue. A downside of

this simple design is that the experiment cannot fully address issues that may occur in a

richer field environment. For example, downstream firms are not represented by subjects in

the experiment and this may preclude effects that work in favor or against the foreclosure

hypothesis.

There are three main experimental results. All three results hold with both random and

fixed matching. Firstly, prices are significantly higher in markets where one firm is vertically

integrated compared to those markets where both upstream firms are separated. Second, if

one firm is integrated, the integrated firms’ pricing behavior is less competitive than that

of nonintegrated firms. Third, despite these anti-competitive effects, integrated firms only

rarely completely foreclose the input market. That is, on the one hand, there is foreclosure

in the broad sense of higher prices for the input, but, on the other hand, there is almost no

evidence of foreclosure in the narrow sense.

5It should be added that the experiments do not provide a formal test of these papers as the experimental

design differs in various dimensions from the frameworks of the formal models.

6

As these results violate the Nash equilibrium prediction, an explanation for the findings

is needed. It turns out the results are consistent with a quantal response equilibrium analysis

of the game (McKelvey and Palfrey [1995]). Quantal response equilibrium takes decision

errors into account, so that players do not choose the best response with probability one but

choose better choices more frequently. Quantal response equilibrium captures the fact that

the vertical merger affects the payoff structure of the game. While this does not change the

standard Nash prediction, it has an impact on the QRE outcomes.

Goeree and Holt [2001] have shown for several games that changes in the payoff struc-

ture that do not affect the Nash prediction can nevertheless have effects on the results of

experiments.6 More closely related to this paper, Capra et al. [2002] analyze experiments

with price-setting duopolies in which the unique Nash equilibrium is the Bertrand outcome.

Competition, however, is not perfect because the market share of the high-price firm is larger

than zero.7 The experimental results show that price levels are positively correlated with the

market share of the high-price firm—which is a violation of the Nash prediction. The results

in Capra et al. [2002], and in most of Goeree and Holt’s [2001] examples, are well explained

by quantal response equilibrium.

For the setting of this paper, quantal response equilibrium implies that integrated firms

do indeed price less competitively than nonintegrated ones. Integrated firms still compete

in the input market (that is, there is no foreclosure in the narrow sense), but the broad

6Goeree and Holt [2001] analyze ten simple one-shot games where the experimental data support the

Nash equilibrium (the “treasure” treatments). For all ten games, they find an “intuitive contradiction”

which results from a change in the payoff structure that leaves the Nash prediction unchanged but drastically

alters the experimental results.

7Morgan, Orzen and Sefton [2006] also ran experiments with imperfect Bertrand competition. In their

model, a firm that is not charging the lowest price still sells a positive amount due to brand-loyal consumers.

Morgan, Orzen and Sefton [2006] analyze how the comparative statics predictions for changes in the degree

of consumer loyalty are borne out in the data.

7

implication of the OSS model—that integration raises the price of the input—is consistent

with the quantal response equilibrium generalization of Nash equilibrium.

2 Experimental Design

To clarify the scope of the experiment, it seems useful to start with a recapitulation of the

moves of OSS’s [1990] foreclosure game as it perceived in the literature (refer to Figure 1 for

firms’ labels again).

1. Firms U1 and D1 decide whether to integrate.

2. Given the integration decision, U1 (or U1-D1) and U2 simultaneously decide about

upstream prices.

3. Knowing upstream prices (and therefore knowing their input costs), D1 and D2 simul-

taneously set downstream prices.

4. Consumers make purchasing decisions given downstream prices.

The second stage of the model is at the heart of the OSS [1990, 1992] papers and the

debate around them, and the experiments are about this second stage only. It is at this point

where OSS [1990] assume that integration enables a firm to commit to a high price or to stay

out of the market whereas the subsequent literature assumes that no commitment is available.

The experiment follows the subsequent literature as pricing decisions are simultaneous moves

without commitment.

The experiment abstracts from the other three stages in order to be as simple as possible.

The first stage is exogenously given in the experiment. There are experimental treatments

with and without vertical integration, and integration is not a choice for the subjects. Neither

the third nor the forth stages are present in the experiments, that is, downstream firms and

final-good consumers were not represented by participants in the experiments. Instead, they

8

are assumed to play according to Nash equilibrium. Downstream firms’ and consumers’

equilibrium behavior implies the payoffs tables that were given to the subjects.

How was this decision problem of the second stage implemented in the experiments? In all

treatments, two subjects representing the two upstream firms have to make one single choice

in every period, they simultaneously set an (upstream) price which has to be an integer

between one to nine. The treatments (integration or separation) differ in the payoff table

that is given to the subjects. These payoff tables are derived from a parametrized model (see

Appendix). The tables are fully consistent with the analysis in OSS [1990] who indeed use

the same parametrized model for some of their analysis.

In the treatments with vertical separation, the basis for the decision making is the profit

table reproduced in Table 1. Here, participants play a Bertrand duopoly experiment (similar

to the first price-setting oligopoly experiments, conducted by Fouraker and Siegel [1963]).

The firm that charges the strictly lowest price will gain the profit in the “Bertrand profit”

cells.8 In the case of a tie, both firms get half that profit. In the instructions, this was

illustrated with two examples, one of which read “If you charge a price of 7 and the other

firm charges a price of 4, you will get zero and the other firm gets 81 pence”.

Price 1 2 3 4 5 6 7 8 9Bertrandprofit

39 54 69 81 90 99 90 72 51

Table 1: The payoff table for the treatments without vertical integration

In the treatments with vertical integration, the two participants play the same Bertrand

game9 but the twist is that one subject (firm 1, the integrated firm) now makes an extra

profit. In these treatments, the basis of decision making is the profit table reproduced in Table

8In the instructions of the experiments, neutral labels were used instead of the terms “Bertrand” and

“integrated firm” (instructions are available from the author upon request).

9One general implication of vertical integration is that the downstream unit of the integrated firm no

longer buys the input from the market but instead obtains it at marginal cost internally. This implies that

9

2. In addition to the “Bertrand profits” (with the rules of the game as above), there is the

“additional profit” in Table 2. This extra payoff represents the profit the downstream affiliate

of the integrated firm earns. This row of the payoff table thus applies to integrated firms

only. Consistent with the theory of OSS [1990], the higher the price in the Bertrand game,

the more “additional profit” the integrated firm earns—this is the raising-rival’s-costs effect.

Thus, as it was put in the instructions, “it is the lowest of the two prices that determines

the [“additional”] profit, no matter whether firm 1 [the integrated firm] or firm 2 (or both)

charged the lowest price”. One of two illustrative examples in the instructions reads: “If firm

1 charges a price of 7 and firm 2 charges a price of 4, firm 1 only gets 96 pence” additional

profit.

Price 1 2 3 4 5 6 7 8 9Bertrandprofit (both firms)

39 54 69 81 90 99 90 72 51

Additional profit(integrated firms only)

66 74 84 96 105 132 159 180 198

Table 2: The payoff table for the treatments with vertical integration

Note, once more, the commitment problem. Ideally, the integrated firm would want to

commit to a price of 7 or higher, because the nonintegrated firm would then best respond by

setting the monopoly price of 6. In that case, profits would be 132 for the integrated firm

and 99 for the nonintegrated firm. However, this foreclosure strategy is not feasible without

commitment, as the integrated firm can obtain 90 + 105 > 132 by deviating to a price of 5.

Thus, absent commitment, vertical integration may not make any difference at all (Hart and

Tirole [1990], Reiffen [1992]).

The experimental markets were designed such that firms still make a positive profit when

they both charge 1 (the Nash equilibrium price, derived below). The reason is that subjects

the input market has a bigger volume with vertical separation (twice as big) and thus the “Bertrand profits”

in Table 1 should also be bigger without integration. However, as the experimental design needs to avoid

possible wealth effects, the “Bertrand profits” are kept equal across treatments (see also Appendix).

10

might be biased against an action with zero profit (Dufwenberg et al. [2007]). Consistent

with the underlying theoretical model, the “additional profit” is larger than the one in the

“Bertrand” row. This means that the integrated firm makes a larger profit than the nonin-

tegrated firm even if it does not get any profit in the Bertrand game.

The two treatment variables are the vertical structure and the matching scheme. The

treatments with and without vertical integration are labeled INTEG and SEPAR , respec-

tively. Treatments where participants were randomly rematched in every period have the

label RAND, and treatments where subjects repeatedly interacted in pairs of two (fixed

matching) are labeled FIX. Table 3 summarizes the 2×2 treatment design.

matchingrandom fixed

separation SEPAR RAND SEPAR FIXvertical

integration INTEG RAND INTEG FIX

Table 3: The treatments

The treatments in Table 3 had a length of 15 periods. As a robustness check, additional

sessions with a length of 25 periods were conducted for the treatments with random matching.

Below, these treatments are referred to as SEPAR RAND25 and INTEG RAND25. In all

treatments, subjects knew the number of periods and the end period from the instructions.

3 Predictions

The subgame perfect Nash equilibrium prediction is the same for all treatments but it seems

worthwhile to go through the four variants in detail separately.

In SEPAR RAND, both firms charge the lowest price of 1 in equilibrium (this is the

standard Bertrand-Nash equilibrium). Equilibria where firms charge a higher price do not

11

exist because firms have a strict incentive to undercut at any price larger than 1. Both firms

earn 39/2 = 19.5 in equilibrium.

In INTEG RAND, the integrated firm would want to commit to a price larger than 6 but

this is not a Nash equilibrium. As emphasized by Hart and Tirole [1990] and Reiffen [1992],

the unique Nash equilibrium has both firms choosing 1 also with vertical integration. In the

equilibrium of this treatment, the nonintegrated firm earns 19.5 and the integrated firm earns

19.5 + 66 = 85.5.

In SEPAR FIX there is repeated interaction and it is well known that some collusion may

occur. If so, the price of 6 would maximize joint profits. In any event, the subgame perfect

Nash equilibrium is for both firms to charge the price 1 just as in the RAND treatments, as

follows from backward induction in the finitely repeated game.

In INTEG FIX, firms may collude by charging the same price. In that case, any price

between 6 and 9 is Pareto efficient (from the firms’ point of view). Vertical integration may

also allow for another form of collusion where firms charge different prices and collude by

coordinating on foreclosure (in the narrow sense). The integrated firms could set a price

larger than 6 and the nonintegrated firm could set a price of, e.g., 6. However, neither way

of colluding is a subgame perfect Nash equilibrium, as follows from backward induction, and

both firms choosing 1 is the subgame perfect Nash prediction once again.

4 Procedures

All treatments were run in sessions with 10 participants. Five participants acted as “firm 1”

(the integrated firm in INTEG treatments) and the other five participants acted as “firm 2”.

These roles were fixed for the entire course of the experiment. In the SEPAR treatments,

firms are symmetric but the “firm 1”–“firm 2” labels were nevertheless given in order to keep

matching scheme and instructions comparable.

There were four sessions (each with ten participants) for treatment SEPAR RAND and

12

also four for INTEG RAND. There was one session each for treatments SEPAR FIX and

INTEG FIX. Having more sessions with random matching is motivated by the possibility of

group effects within sessions under random matching.

Experiments were computerized, with the programming done in z-Tree, developed by

Fischbacher [2007]. The treatments listed in Table 3 were conducted at Royal Holloway

College, University of London, in autumn 2004 and spring 2005. The payoffs in Tables 1 and

2 denote cash payments British pence. Subjects’ average monetary earnings were £12.50,

including a flat payment of £5 in the London sessions. In total, 140 subjects participated

(100 in the main treatments plus 40 in the sessions with 25 periods, reported below in Section

6). Subjects were mainly undergraduate students and a large proportion of them were from

faculties other than economics or business studies.

5 Results

Table 4 and Figures 2 and 3 summarize the results10 The averages in Table 4 and most formal

tests are based on data from periods 6 to 15. All results reported also hold qualitatively if

the analysis is based on all periods or on periods 11 to 15. There are four entirely indepen-

dent observations for the RAND treatments and five independent observations for the FIX

treatments. The non-parametric tests applied here (in this case, Mann-Whitney U tests)

conservatively only use these four and five observations, respectively.11

10Based on the main treatments with 15 periods length. The results from the treatments with 25 periods

length are reported below.

11Nonparametric tests are distribution-free tests that do not rely on assumptions regarding the distribution

the data are drawn from (e.g., normal distribution). The tests work with cardinal rankings of the observations

rather than ordinally measured data. See, for example, Hollander and Wolfe [1999].

13

0

1

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Period

Av

erag

eP

rice

SEPAR_RAND

INTEG_RAND

5

6

INTEG_FIX

Figure 2. Average prices in SEPAR (dashed lines) and INTEG(solid lines) for random matching (top panel) and fixed

matching (bottom panel)

0

1

2

3

4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Period

Av

erag

ep

rice

SEPAR_FIX

Figure 2: Average prices in SEPAR (dashed lines) and INTEG for random matching (toppanel) and fixed matching

.

vertical structureSEPAR INTEG

RAND1.81

(0.43)2.83

(0.77)p = 0.021

matching

FIX2.67

(1.15)4.40

(1.02)p = 0.014

p = 0.115 p = 0.033

Table 4: Average prices (based on session and group averages, standard deviation in parenthesis)and (one-sided) p-values of Mann-Whitney U tests for differences between the price distributions

of the treatments

14

Prices in SEPAR RAND are lower than those in INTEG RAND. The top panel of Figure

2 confirms this for the average prices in SEPAR RAND and INTEG RAND across the 15

periods and Table 4 shows that prices are about 36% higher with vertical integration. The

significance of this result follows from a Mann-Whitney U test (p = 0.021, see also Table 4).

The top panel of Figure 3 indicates that there are some differences between the prices

of integrated and nonintegrated firms in INTEG RAND. Averaging across periods 6 to 15,

integrated firms’ prices are about 8% higher with random matching. These differences are

significant (one-sided matched-pairs Wilcoxon, p = 0.034) although quantitatively perhaps

not particularly big.

0

1

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Period

Av

erag

ep

rice

integrated firms

nonintegrated firms

6integrated firms

RANDOM

FIXED

Figure 3. Average prices of integrated firms (solid lines) and nonintegratedfirms (dashed lines) in the INTEG treatments, random matching (top panel)

and fixed matching (bottom panel)

0

1

2

3

4

5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Period

Aver

age

pri

cera

nonintegrated firms

Figure 3: Average prices of integrated firms (solid lines) and nonintegrated firms in theINTEG treatments, random matching (top panel) and fixed matching

15

Essentially the same results also hold in the FIX treatments. Comparing SEPAR FIX

and INTEG FIX, Figure 2 and Table 4 indicate differences due to integration which are

quantitatively bigger than with random matching. The relative increase is roughly the same,

however, as prices are about 39% higher with integration in FIX. These differences are sig-

nificant (p = 0.014). As with random matching, integrated firms in INTEG FIX charge 8%

higher prices than nonintegrated firms (significant according to a matched-pairs Wilcoxon,

p = 0.039). (See below for an analysis of whether this results holds with a longer horizon.)

Result 1: There is evidence of foreclosure broadly defined. Markets with a vertically integrated

firm have significantly higher prices than markets where the two firms are separated. In

markets with integration, the vertically integrated firms charge significantly higher prices than

the nonintegrated firms.

How about foreclosure in the narrow sense then? Strong evidence in favor of that would be

if integrated firms charged a price higher than 6, as this would imply a complete withdrawal

from the input market.

It is already clear from Figures 2 and 3 and the averages in Table 4 that there is only

little evidence of such behavior, and a concrete search for these foreclosure outcomes confirms

that they are rare. In INTEG RAND, only one of 20 subjects representing an integrated

firm charged prices which deviated from the general pattern visible in Figure 2. This subject

charged prices of 7 and 8 from period 2 to 13 and clearly did not compete in the input market

except for the last two periods. This can be interpreted as foreclosure behavior, narrowly

defined. In total, however, only 29 of 300 observations (data from all periods) include prices

of 7 or higher, and 12 of these cases are accounted for by the subject just mentioned. For

comparison, nonintegrated firms in INTEG RAND charged a price of 7 or higher in 4 (of

300) cases, and in SEPAR RAND there were 11 (of 600) such observations. Hence, whereas

these shares are somewhat lower than those of the integrated firms in INTEG RAND, too

few observations in INTEG RAND are consistent with (narrow) foreclosure to suggest that

it is important in the data.

16

In treatment INTEG FIX, integrated firms charged prices of 7 or higher in 5 of 75 cases.

Compared to this, nonintegrated firms did so in 2 of 75 cases, and in SEPAR FIX there are

5 (of 150) such cases (data from all periods). Hence, INTEG FIX does not contain more

evidence of foreclosure in the narrow sense than INTEG RAND does.

Looking at the five individual duopoly pairs in INTEG FIX yields further insights.

Duopoly #1 had both firms charging a collusive price of 6 in all periods except for the

first two and the last three. Duopoly #2 priced competitively in the first and last third of

the experiment and only in two outcomes in the middle of the experiment did the integrated

firm charge high prices. Duopoly #3 colluded non-systematically. Sometimes, there was

symmetric collusion, sometimes there were apparently competitive outcomes with either firm

being the low-price firm. In duopoly #4, the integrated firm never charged a price lower than

the rival, possibly suggesting a foreclosure strategy—but then, why did this firm not go all

the way and set a price above 6? Finally, duopoly #5 started competitively and then colluded

symmetrically at a price of 6. To summarize, there is not more evidence of foreclosure with

fixed matching either. If firms collude successfully at all, they both tend to choose a price of

6 rather than have the integrated firm foreclose the input market.

TreatmentLow-price firm INTEG RAND INTEG FIX

integrated 32% 22%nonintegrated 39% 40%

ties 29% 38%# observations 200 50

Table 5: Number of observations when the integrated firm or the nonintegrated firm charged thelowest price, and number of ties.

Even if integrated firms do not charge prices higher than 6, it could still be that they do

not compete and that they only rarely charge a lower price than nonintegrated firms as a

17

result. Table 5 shows data on which type of firm turns out to be the low-price firm in the IN-

TEG treatments (in periods 6–15). The table also lists the number of ties. Integrated firms

charge the lowest price less frequently than nonintegrated firms both in INTEG RAND and

INTEG FIX. These differences are significant according to binomial tests in INTEG RAND

(p = 0.0625, one sided) and INTEG FIX (p = 0.03125, one sided).12 However, while con-

sistent with Result 1, they are quantitatively too minor to support the narrow foreclosure

hypothesis.

Result 2: There is little evidence of foreclosure narrowly defined. Even though integrated

firms are the low-price firm significantly less often, they still compete actively in the input-

good market.

6 Robustness Check: Games with 25 Periods

Both Figure 2 and Figure 3 indicate a negative time trend in the data. In INTEG FIX,

prices are stable except for an end-game effect in the last three periods. Regarding IN-

TEG RAND and SEPAR RAND, however, it could be that both treatments converge to the

Nash equilibrium price of 1 only at different rates. In that case, Result 1 would not be robust.

To check for the impact of the length of the horizon, additional sessions with a length of 25

periods were carried out in the spring of 2010 at the University of Duesseldorf. Specifically,

there were 40 subjects participating in two sessions each for treatments SEPAR RAND25

and INTEG RAND25.

The data from treatments INTEG RAND25 and SEPAR RAND25 indicate that with

12Integrated firms charge the lowest price less frequently than nonintegrated firms in all four (five) groups

of INTEG RAND (INTEG FIX ). Accordingly, a binomial test rejects the null hypotheses of equal likelihood

at a significance level of p = (1/2)n, where n is the number of observations.

18

a longer horizon the above results remain.13 In periods 16 to 25, average prices in IN-

TEG RAND25 are 2.51, and they are 1.46 in SEPAR RAND. Importantly, there are no

significant time trends in this phase of the experiments any more with Spearmen corre-

lations coefficients (of prices and time) being ρ = −0.105 (p > 0.1) in INTEG RAND25

and ρ = 0.085 (p > 0.1) in SEPAR RAND25. (Average prices in periods 6 to 15 suggest

more pronounced differences than in the main treatments with average prices of 1.43 in

SEPAR RAND25 and 3.06 in INTEG RAND25 ). Thus, these averages suggest that the dif-

ferences persist.14 On the other hand, the differences are arguably quantitatively weak, and

it is not clear how the effect of a vertical merger would carry over to a more complex setting

in which other effects may confound the foreclosure effect.

7 Quantal Response Equilibrium Analysis

The results suggest that vertical integration has an impact. We saw that integrated firms

charge significantly higher prices. This effect was sufficient to render less competitive the

markets where vertical integration is present. While this confirms the OSS [1990] hypothesis

in a broad sense, the lack of evidence for foreclosure rejects the narrow OSS prediction. How

13Note that extending the length of the experiment is not without cost. The longer the horizon, the more

the game may have aspects of a repeated game, despite the random matching scheme. (Subjects may simply

recognize that they interact “many” times with the individual members of the group, even if each interaction

is randomly determined). There is a tradeoff between the goal of a longer horizon and avoiding repeated-game

effects.

14Because only two (randomly rematched) sessions were conducted for each treatment of this robustness

check, one cannot conduct the non-parametric tests applied above. However, the significance of the result

in periods 16 to 25 can be explored by running t-tests on average prices. Counting each individual as one

observation, one can establish a lower bound for the significance value at p < 0.001 (t = −4.40). With just

one average price for each session, the result is weakly significant at p = 0.051 (one sided, t = −1.85).

19

can these results be accounted for?

In this section, it will be argued that the above findings are consistent with the quantal-

response equilibrium (QRE) analysis (McKelvey and Palfrey [1995]) of the game. QRE is

a generalization of Nash equilibrium that takes decision errors into account. Players do not

always choose the best response with probability one but they do choose better choices more

frequently. Because of this, changes in the payoff structure that do not affect the standard

Nash prediction can still have an impact on the QRE outcome(s). In the model of this paper,

vertical integration (compared to nonintegration) has exactly this impact. Therefore, QRE

is a good candidate for explaining the results.

Consider the logit equilibrium variant of QRE. Firm i, i = 1, 2, believes that the other

firm will choose price pk, k ∈ {1, 2, ..., 9}, with probability ρki . Accordingly, firm i’s expected

profit from choosing price j is

Πji =

9∑k=1

ρki πi(pj, pk), j = 1, ..., 9.

where πi(pj, pk) are the profits as in the Bertrand game of Table 1 (note that profit functions

are not symmetric in the INTEG treatments). As mentioned above, firms choose better

choices more frequently. In particular, choice probabilities, σji , are specified to be ratios of

exponential functions

σji =eλΠj

i∑9k=1 e

λΠki

, j = 1, ..., 9.

λ is the error parameter. If λ = 0, behavior is completely noisy and all prices are equally

likely regardless of their expected profit. As λ → ∞, firms choose the best response with

probability one. In the logit equilibrium, beliefs and choice probabilities have to be correct,

that is, ρj1 = σj2 and ρj2 = σj1, j = 1, ..., 9.

Using Gambit (McKelvey et al. [2005]), a unique equilibrium (given λ) is found, as il-

lustrated in Figure 4. The figure shows the relative frequency of the price of 1 in QRE

conditional on the error parameter, λ. The impact of λ is intuitive. If λ = 0, the price of

1 (like any other price) is chosen with probability 1/9 and, as λ → ∞, it is chosen with

probability one, as in the standard Nash equilibrium. When λ ∈ (0,∞), vertical integration

20

implies (among other things) that the frequency of the price 1 is lower than in markets with

separation. Only when λ = 0 and λ → ∞, does vertical integration not have any impact.

The figure illustrates these findings for a relevant range of lambda. It also shows that the

integrated firms in INTEG set the price of 1 less often than nonintegrated firms.15

0%

20%

40%

60%

80%

100%

0.049 0.070 0.095 0.123 0.153 0.187 0.230

Fre

qu

ency

of

of

p=

1

λ

SEPAR

INTEG

integratedfirm

nonintegratedfirm

Figure 4. Quantal Response Equilibrium simulations for the frequency ofFigure 4. Quantal Response Equilibrium simulations for the frequency ofthe price of 1.

Figure 4: Quantal Response Equilibrium predictions for the frequency of the price of 1

To summarize up to this point, whereas neither the static Nash equilibrium nor the

foreclosure outcome organize the data in the RANDOM treatments well, QRE does. The

qualitative predictions of QRE are confirmed. In particular, the QRE analysis is consistent

with the finding that, although integrated firms charge somewhat higher prices, they do not

completely refrain from competing in the input market.

What is the intuition behind the mechanics of the QRE analysis, and why can it explain

15This can be generalized. It turns out that, for any λ ∈ (0,∞), the distribution of the prices of the

nonintegrated firm first-order stochastically dominates that of integrated firms in the INTEG setup. This

supports the claim that integrated firms are less competitive than their nonintegrated counterparts. However,

it does not generally follow that prices will be lower in SEPAR compared to INTEG (in the sense of first-order

stochastic dominance).

21

treatment differences? As mentioned above, players do not play a best reply with certainty in

QRE and prices higher than the Nash equilibrium price are played with positive probability—

however, this applies to both treatments with and without integration. The key difference

vertical integration makes is that the integrated firm loses less profit when the rival undercuts

its price. Therefore, integrated firms charge higher prices (in a probabilistic sense) and this

also pushes up the prices of non-integrated firms in equilibrium (where expectations are

correct), rendering the INTEG treatments less competitive. Put in terms of the foreclosure

story, an integrated firm still has an incentive to compete (which confirms Hart and Tirole

[1990] and Reiffen [1992]) but that this incentive is weaker than for a nonintegrated firm

(which confirms OSS’ broad foreclosure interpretation).

The next step is to estimate λ. Using data from INTEG RAND and SEPAR RAND

jointly,16 Maximum-Likelihood estimates of the error term are as follows. For periods 6 to

15 (which the results in the above section were based on), λ = 0.134 results with a standard

error of 0.006. Intuitively, the λ estimates increase over time. In periods 1 to 5, λ = 0.051

(0.012) results; whereas, in periods 11 to 15, λ = 0.182 (0.009) is the estimate. This is

consistent with the decline in prices observed in the RAND treatments and the notion that

subjects learn over time and become “more rational”.

How well do QRE and the actual estimate of λ fit with the differences observed between

the two treatments (INTEG RAND and SEPAR RAND)?

16Note this yields one Maximum Likelihood estimates of λ for two treatments (INTEG RAND and

SEPAR RAND). Recently, Haile et al. [2008, p. 188] have criticized that “[a]lthough many papers have

examined the fit of the logit QRE in different treatments (varying payoffs), typically a new value of the

logit parameter is estimated each time.” Here, a single estimate is conducted only, and it can rationalize

the observed difference between the two treatments. Haile et al. [2008, p. 188] explicitly do not criticize

this. Note also that QRE arguments generally have less bite in repeated-game settings because there is less

uncertainty about the action of the other player. Therefore, the estimations are based in the data from the

RAND treatments.

22

• The predicted (expected) average QRE price in SEPAR RAND is 2.13, and the actual

average turns out to be 1.81. In INTEG RAND, predicted average prices are 2.89 and

2.23 for the integrated and nonintegrated firm, respectively. Observed average prices

of 2.96 and 2.71.

• The expected winning price (the minimum of the two prices) is predicted to be 1.30

in treatment SEPAR RAND and the actual average is exactly 1.30. In INTEG RAND

the prediction is 1.57 and the average is 2.17 .

Whereas the broad magnitude of expected values corresponds to the actual values, it ap-

pears that the QRE prediction (given λ = 0.134) somewhat overestimates the differences

between integrated and nonintegrated firms and underestimates the differences between the

treatments’ averages.

Note that QRE implies a distribution for the prices firms charge that differs between the

treatments, given the estimate λ = 0.134. (By contrast, if firms merely made decision errors,

a uniform distribution across prices would result in both treatments.) In SEPAR RAND,

the QRE predicted and observed frequency of prices are as follows. Price of 1: 50% (QRE)

and 55% (data); price of 2: 20% and 29%; prices larger than 2: 16% and 30%. The same

numbers for INTEG RAND are like this. Price of 1: 32% (QRE) and 24% (data); price of 2:

28% and 27%; prices larger than 2: 40% and 50%. It appears that the QRE predicted and

the observed distribution do not differ substantially. But, more importantly QRE, seems to

capture the treatment differences rather well on basis of the same estimate for λ.

8 Conclusion

This paper contributes to the literature on vertical integration and raising rivals’ cost with

the use of a laboratory experiment. The experiments were designed to analyze the raising-

rivals’-costs argument of Ordover, Saloner and Salop [1990]. In simple duopoly treatments

(with random and fixed matching), the data show how the presence of an integrated firm

23

affects market outcomes.

The experimental results support the hypothesis of Ordover, Saloner and Salop [1990] in

that overall competition is reduced when one firm vertically integrates and, in markets where

an integrated firm is present, it charges higher prices compared to nonintegrated firms. While

the effects are quantitatively small, they are statistically significant. On the other hand, there

is very little evidence of foreclosure in the sense that virtually no integrated firm completely

refrains from competing in the input market. Whereas these results are inconsistent with the

standard notion of Nash equilibrium, these results are consistent with the quantal response

equilibrium (McKelvey and Palfrey [1995]) generalization of Nash equilibrium. The results

are also consistent with Ordover, Saloner and Salop’s [1992] broad notion of foreclosure which

says that vertical integration generally causes an anticompetitive effect even if no refusal to

supply the input market is observed.

The lack of evidence for foreclosure (narrowly defined) suggests that the commitment

problem of the integrated firm pointed out by Hart and Tirole [1990] and Reiffen [1992] is

significant. In experiments, participants do generally not manage to resolve commitment

problems simply with mere intentions. This has been found in Huck and Muller [2000],

Reynolds [2000], Cason and Sharma [2001] and Martin, Normann and Snyder [2001].17 In

these experiments, subjects failed to achieve desirable outcomes when there was no formal

commitment mechanism, and the same appears to be the case in this study.

Further investigating the commitment issue also seems promising for future research. For

example, will firms commit if they are given the opportunity to do so? Likewise, will firms

learn to commit if they are forced to do so over a transitory period? Further, one could

17Huck and Muller’s [2000] experiments show that a Stackelberg leader has serious difficulties exploiting

the first-mover advantage when second movers obtain a noisy signal of its action. Reynolds [2000] and Cason

and Sharma [2001] show that monopolies producing durable goods often fail to achieve full monopoly profits.

Similarly, in the experiments of Martin, Normann and Snyder [2001], a firm loses its monopoly power when

selling its product through multiple retailers.

24

imagine effects arising in a more complex environment that seem worth investigating. When

both upstream and downstream competition are part of the experiment, how will this affect

the firm that explicitly makes both upstream and downstream decisions, and how integrating

previously separate firms influence pricing behavior?

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Appendix: The model

This appendix presents the model underlying the payoff table of the experiment. The model

has two upstream firms (U1 and U2) which are Bertrand competitors and two downstream

firms (D1 and D2) which transform the input into differentiated final goods.

27

We begin at the downstream level. Downstream firm Di’s demand is

qi(pi, pj) = a− bpi + dpj; i, j = 1, 2; i 6= j, (1)

where pi and pj are the prices the downstream firms i and j set (i, j = 1, 2; i 6= j). Suppose

downstream firm i purchases the input good at a linear price of ci per unit. As the D

firms incur no other costs, they operate at constant marginal costs of c1 and c2, respectively.

Thus, at the downstream level, this is a standard Bertrand duopoly model with product

differentiation and asymmetric cost. It is straightforward to solve for downstream Nash

equilibrium prices

p∗i (ci, cj) =(2b+ d)a+ 2b2ci + bdcj

4b2 − d2, (2)

outputs

q∗i (ci, cj) = b(2b+ d)a− (2b2 − d2)ci + bdcj

4b2 − d2, (3)

and profits π∗Di = (q∗i (ci, cj))2/b.

Upstream firms have constant marginal cost which are assumed to be zero for simplicity.

The upstream firms compete for each of the two downstream markets in a Bertrand fashion.

Specifically, upstream firm k sets two prices, cUk1 and cUk2 , for downstream firms 1 and 2,

respectively. The Bertrand logic implies that the downstream firm i buys from the upstream

firm with the lowest price, formally ci = min{cU1i , cU2

i }, i = 1, 2. Put it another way, an

upstream firm will sell a positive amount to Di only if it charges the lowest price. Formally,

when upstream firm k bids cUki to downstream firm i, it will make the following profit with

Di

πUki (cUki , cUli ) =

cUki q∗i (c

Uki , cUki ) if cUki < cUli

cUki q∗i (cUki , cUki )/2 if cUki = cUli

0 if cUki > cUli

(4)

where k, l = 1, 2; k 6= l; i = 1, 2.

When neither firms is integrated, in the general model, U1 and U2 set prices (cU11 , cU1

2 )

and (cU21 , cU2

2 ), respectively. For the derivation of the payoff tables, c1 is set equal to zero. The

reason is that c1 = 0 with vertical integration. Thus, in order to keep treatments comparable

and avoid wealth effects, one also needs c1 = 0 without integration. Essentially, this is implies

that firms only compete for D2 also absent integration. This is without loss of generality of

the qualitative features of Bertrand competition are unaffected by this. D2 buys at the lower

of the two prices such that c2 = min{cU12 , cU2

2 }. Next, given c1 = 0 and c2, D1 and D2 set

the final good prices. In equilibrium, D1 and D2 charge p∗1(0, c2) and p∗2(c2, 0), respectively.

Downstream profits are π∗D1 = (q∗1(0, c2))2/b and π∗D2 = (q∗2(c2, 0))2/b, and upstream profits

are πU12 , πU2

2 and πUk1 = 0.

28

A vertical merger of U1 and D1 implies that the integrated firm’s true input price is

U1’s marginal cost (Bonanno and Vickers, 1988). Thus, D1 will be delivered efficiently at

c1 = 0 and U2 cannot compete for the D1 business any more. For both upstream firms,

only the D2 market remains a source for potential business. Profits are as follows. D2

earns π∗D2 = (q∗2(c2, 0))2/b, U2 earns πU22 , and the integrated firm U1-D1 makes a profit of

πU12 + π∗D1 = πU1

2 + (q∗1(0, c2))2/b.

Tables 2 and 3 can be derived from these closed-form solutions for the parameters a =

35/2, b = 4, d = 2. The actual price parameters used to derive the profits in the table differ

from the prices labels “1” to “9”. In particular, profits around the joint-profit maximizing

prices are quite flat. Hence, prices were increased in steps larger than one in this range to

avoid the “flat-maximum” critique (Harrison, 1989). The actual price parameters underlying

the values in the table are {1.1, 1.6, 2.2, 2.9, 3.5, 5.0, 6.5, 7.6, 8.5}. Additionally, profits were

multiplied by three and rounded to yield the payoff in real currency subjects received.

29

PREVIOUS DISCUSSION PAPERS

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03 Wenzel, Tobias, Deregulation of Shopping Hours: The Impact on Independent Retailers and Chain Stores, September 2010.

02 Stühmeier, Torben and Wenzel, Tobias, Getting Beer During Commercials: Adverse Effects of Ad-Avoidance, September 2010.

01 Inderst, Roman and Wey, Christian, Countervailing Power and Dynamic Efficiency, September 2010.

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